Lack of near-sightedness principle in non-Hermitian systems

TL;DR

This paper reveals that the non-Hermitian skin effect does not follow the traditional bulk-edge correspondence, showing that local impurities can significantly alter boundary state accumulation without affecting bulk invariants.

Contribution

It demonstrates that the non-Hermitian skin effect can be suppressed or depleted by local impurities, indicating weaker bulk-edge correspondence than previously thought.

Findings

Skin modes are depleted at boundaries by impurities.

Impurities can cause accumulation at specific sites.

Bulk invariants remain unchanged despite boundary effects.

Abstract

The non-Hermitian skin effect is a phenomenon in which an extensive number of states accumulates at the boundaries of a system. It has been associated to nontrivial topology, with nonzero bulk invariants predicting its appearance and its position in real space. Here, we demonstrate that the non-Hermitian skin effect has weaker bulk-edge correspondence than topological insulators: when translation symmetry is broken by a single non-Hermitian impurity, skin modes are depleted at the boundary and accumulate at the impurity site, without changing any bulk invariant. Similarly, a single non-Hermitian impurity may deplete the states from a region of Hermitian bulk.